Workshop 4: Neuromechanics of Locomotion: Abstracts and Lecture Materials
A multi-level approach is needed to understand how the in vivo dynamics of muscle-tendon units, which operate at specific joints within an animal's limb, are integrated in terms of overall limb and whole-body dynamics. Rapid adjustments to destabilizing perturbations are likely facilitated by intrinsic force-velocity and force-length properties of the muscle and tendon, prior to neural feedback. Subsequent modulation of motor output via reflexes can then provide more robust, ongoing control. Differences in muscle-tendon architecture suggest that a proximo-distal gradient of neuromotor control may operate within the limbs of vertebrate animals, with proximal muscles hypothesized to operate under feedforward control and distal muscles via intrinsic and feedback control. Overall, a simple mass-spring model of the body supported on a limb spring describes well the mechanical behavior of both steady and perturbed animal running.
Ultimately, stabilization and economical movement require control of forces and moments exerted about an animal's body center of mass (CoM). These result from the temporal pattern of limb-ground reaction forces and limb placement. Quadrupedal gaits of terrestrial mammals are designed to reduce pitch, roll and yaw moments, but pitch moments are greatest for both trotting and galloping. Understanding how these moments change in response to a perturbation or for maneuvering will guide biorobotic strategies for controlling limb position, end-point limb forces and movement patterns.
(work supported by NIH and DARPA)
The legged systems of animals are driven by muscles. Muscular properties and movement are strongly intertwined and its relationship frequently has been the subject of investigations. In concurrence, the layout of the skeleton and the properties and arrangement of the muscle within the system decide whether the system is able to reach performance goals such as fast acceleration, high velocity or just economic displacement. The term "Neuromechanics" directs our focus onto the interrelationship between control and mechanics or the controllability of a mechanical system. In recent years it could be demonstrated that intelligent constructions can largely facilitate control. Self-stable systems can perform tasks without making use of neuronal feedback. We claim that the muscle-skeletal-system of animals as well as its neuronal control is adapted to take advantage of self-stability in order to reduce control effort and to increase robustness. Attractivity within the behavior of a dynamical system can be observed in simple nonlinear systems (e.g. Seyfarth et al., 2002) and does not require a complex element such as the skeletal muscle. Nevertheless, the locomotor system of animals depends on the properties of its drive. Under certain conditions these properties can support self-stability.
Muscles can be considered as force-controlled dampers (Gunther and Schmitt, submitted). In fact the inherent damping properties of the muscle expressed in the force-velocity relation are crucial for the muscle-skeletal system to stabilize after a perturbation. The simplest task of a muscle might be to balance a load via a lever arm. A closely related natural situation can be found for example in the forearm when a waiter holds his tray. Subjecting the system to perturbations, e.g. by walking, should result neither in spilling the water nor in dropping the tray. Critical damping seems to be desirable for this task requiring suitable adjustment of the damper. Provided that the capability to generate force is sufficient the damping depends on the curvature of the force-velocity relationship of the muscle and the dimensionless maximum system contraction velocity. Slow muscles with strong curvature and low maximum contraction velocity seem to be much better suited to dampen oscillations in this system and may in general be used to maintain posture. In contrast systems with fast muscles generally involved in dynamic movements are prone to ring (Rode et al., 2008). Current experiments are set up to verify this prediction.
In an oscillating system quasi elastic constituents are essential. In a muscle quasi elastic behavior is mimicked by the force-length curve. In fact stable fixed points are only observed at the ascending limb of this curve, fixed points on the descending limb are non-stable (Rode et al., 2008). Force, length, and velocity are affected by the gearing ratio or the effective mechanical advantage (EMA) of the system. Again the advantage must not disrupt the condition of sufficient force, the operation at the ascending limb of the force-length curve of the system, and not transmit velocities to insignificant values. While considering stabilizing conditions it is essential to take the gearing into account. But what about situations in which the gearing changes dramatically? Even in the seemingly simple situation of the waiter with a tray this critical situation occurs (Blickhan et al., 2003). In a strongly flexed arm the EMA for the flexor group is increasing when the glass is put on the tray. In an almost extended situation the situation reverses and the waiter runs into the danger to drop his tray. The situation in the knee joint is even worse as the EMA approaches zero for the extended leg (Wagner and Blickhan, 1999). There a sliding axis of rotation helps to some extent. Nevertheless, a dramatic improvement is achieved by introducing co-activated antagonists (Wagner and Blickhan, 2003). Above that this expensive strategy allows to actively adjust the range of stability. From walking to running the mechanical advantage of muscles changes strongly (Biewener et al., 2004). Recent investigations on individual jumping strategies in our lab (Ertelt, 2008) have shown that trained jumper have different strategies for recruitment facilitating control and allow for the extension to be supported by biarticular flexors. The jumpers employ biarticular muscles and take advantage for a changing relation between the levers at the two joints. It is to be expected that this also influences stability of the leg in different geometries.
The field of Neuromechanics adresses the interaction of neuronal control and the mechanics of the substrate. During ontogeny or phylogeny the muscle-skeletal-system may adapt to operate robustly in the presence of internal and external disturbances. In turn the nervous system may learn to explore the attractivity of the muscle-skeletal system.
Work done in collaboration with Christian Rode, Thomas Ertelt, Michael Ernst, Tobias Siebert, and Heiko Wagner.
References:
- Blickhan, R., Wagner, H., Seyfarth, A. (2003) Brain or muscles. In: Pandalai, S.G. (Ed.) Recent research developments in biomechanics 1. Transworld Research Network, Thiru-anantha-puram (Trivandrum), India pp:215-245
- Biewener, A. A., Farley, C. T., Roberts, T. J., Temaner, M. (2004) Muscle mechanical advantage of human walking and running: Implications for energy cost. J. Appl. Physiol. doi:10.1152/ japplphysiol.00003.2004
- Ertelt, T. (2008) Kraftmorphologie der menschlichen Beinbewegung. Hamburg, Verlag Dr. Kovac
- Gunther, M., Schmitt, S. (submitted) A macroscopic ansatz to deduce the Hill relation.
- Seyfarth, A., Geyer, H., Gunther, M., Blickhan, R. (2002) A movement criterion for running. J Biomech 35:649-655
- Wagner, H., Blickhan, R. (1999) Stabilizing function of skeletal muscles: an analytical investigation. J. theoret. Biol. 199:163-179
- Wagner, H., Blickhan, R. (2003) Stabilizing function of antagonistic neuromusculoskeletal systems: an analytical investigation. Biol. Cybern. 89:71-79
Walking movements result from the interaction of central pattern generating networks (CPG), local sensory feedback about movements and forces generated in the legs and coordinating signals from neighboring limbs. I investigated in the stick insect the intersegmental information transfer for activation and coordination of pattern generating networks using reduced preparations with single and multiple legs stepping and pharmacological treatment to activate thoracic CPGs.
My presentation will report the following findings from these studies:
- Activation of segmental CPGs: Only a stepping front leg is able to activate CPGs in the next posterior segment: Single front leg stepping activates the TC-joint CPG in the ipsilateral mesothoracic segment eliciting alternating activity in protractor and retractor motoneurons (MNs). TC-MNs of all other segments, however, including the ipsilateral metathorax only show a general tonic activity increase with one front leg stepping. The situation was reversed for backward walking, when hind leg stepping was able to induce rhythmicity in mesothoracic TC-MNs. In contrast, activation of the metathoracic TC-joint CPG required stepping of both ipsilateral front and middle legs.
- Intersegmental coordination: There appears to exist an intersegmental coupling influence between a stepping front leg and all posterior segments. Upon activation the three homologue TC-joint MN pools were active in phase with each other. These results express marked similarities to the situation in intersegmental coupling between pattern generating networks reported for other animals e.g. swimmeret beating in crustaceans, crawling in manduca larvae and intersegmental coordination in the lamprey spinal cord.
- Preliminary results on the intrasegmental order of activation and coupling of the different joint CPGs support the notion that the individual segmental CPGs are activated in an orderly fashion from the CPGs driving proximal joints to CPGs driving distal joints.
- Currently we are investigating by means of generating phase response curves the intra- and intersegmental influences of specific sensory signals, e.g. local load feedback for coordinating joint CPG activity in the stick insect. Such data will be useful to create realistic computer simulations trying to test the present hypothesis on the role of sensory influences.
In walking each leg movement results from a contribution of descending signals from the brain, central pattern generating networks (CPG), local feedback from sensory neurons about movements and forces generated in the legs, coordinating signals from neighboring limbs, and finally, the neuromuscular transform at the output stage of the walking system, the leg muscles. We have in recent years made significant advances in understanding the neural basis of insect walking. My talk will summarize the current knowledge of the organization and operation of neural networks in the thoracic ganglia generating single leg stepping. I will also outline our current knowledge on (i) how the leg muscle control system changes speed and walking direction and (ii) the neural mechanisms contributing to intersegmental activation and coordination. In doing so, I will highlight those areas, in which information is presently still too sparse to generate sufficient concepts on neural control mechanisms and in which simulation studies will be most useful. I will place current knowledge from the stick insect into the broader context of locomotor behaviors in other organisms.
Among vertebrates, adult salamanders are ideally suited for investigating the neural mechanisms for the adaptation of the locomotor behaviour to the demands of the environment. Indeed, salamanders are tetrapods living both in aquatic to terrestrial habitats, and, accordingly, they are able to exhibit spontaneously two locomotor modes: swimming and terrestrial stepping. Moreover, salamanders diverged from the main vertebrate line around 350 million years ago and are regarded as most closely resembling early terrestrial vertebrates. Therefore, they also provide a useful model to infer the changes in the locomotor circuits that occurred during vertebrate evolution.
To address these issues we have combined in vivo and in vitro neurobiological studies in salamander, and numerical modelling the salamander's spinal cord that we have implemented and tested on a salamander-like robot capable of swimming and walking.
The purpose of this talk is to review our current knowledge about the organisation and the intrinsic operation of the spinal networks underlying swimming and stepping ("Central Pattern Generators"), and the mesencephalic control of gait transition in salamander. In an accompanying presentation, Prof. A.J. Ijspeert will present a model of the salamander's CPG, and its implementation in an amphibious robot in order to test our hypotheses on the neural mechanisms by which salamanders modulate velocity, direction, and gait transition in real physical conditions.
In this presentation, I will describe a range of experiments by many people in many preparations that demonstrate the general organization of motor (and sensory) systems. These studies show that across invertebrates and vertebrates and across the nervous system there is massive feedback among the parts. Within motor systems, there are the well known feedback loops of sensors back to the motor neurons and their interneuron's, but there is also feedforward from the interneurons to the sensors. Furthermore, there is the well known feedforward of the descending systems to the spinal cord, but there is also feedback from the spinal cord to the same descending systems. In both of these loops there is considerable evidence for a positive feedback. In some cases the gain on that feedback loop has been estimated to be less than 1, but in others it clearly is not. This kind of organization is also seen in sensory systems in the brain. In these systems, as well, there is little understanding of the role played by the mutual interactions. The mathematics of all the various interactions is not well developed for a variety of reasons, not the least of which being that the biological details are under determined. With more evidence of the input-output mappings connecting the two systems it will be easier to model the control played by the respective loops. There are likely to be mathematical challenges, as these models will by necessity be non-linear, but they are unlikely to be insurmountable.
How do neural systems process sensory information to control locomotion? To answer this question, we consider two systems: high-speed wall following in the American cockroach, and refuge tracking in weakly electric knifefish. Both systems involve the stabilization of images on sensory arrays: cockroaches "steer" so as to keep their "head-to-wall" antenna distance measurement constant, and knifefish swim to minimize optic and electrosensory flow to remain inside a longitudinally moving tube. In both cases, we use a model of the locomotor mechanics, together with a set of behavioral sensorimotor perturbations, to infer how sensory information is processed to control the underlying locomotor behavior. We then use these models of sensory processing to guide neurophysiological experiments and to understand the mechanisms of neural processing. Our analysis of these two systems suggests a general framework that can be applied across taxa to decode multisensory locomotor control strategies in animals.
Very much like vertebrates, many insects use their limbs in goal-directed motor behaviours that require aiming of the foot. Such goal-directed behaviours include catching prey, reaching for foothold or grooming the body. Here, we describe a model that can explain aimed grooming movements of a locust hind leg. When their wing is touched, desert locusts (Schistocerca gregaria) move their ipsilateral hind leg towards the stimulus site. During the first 200 ms, this movement has a fairly straight trajectory and is well-aimed towards the stimulus site. This aimed part of the movement is followed by a cyclic movement that can last for several seconds. Although this movement is commonly described as grooming, it is typically devoid of contacts with the wing and, therefore, essentially an open-loop movement with regard to the stimulus site.
Since the movement pattern changes continuously in space as the stimulus site is shifted along the body surface, this behaviour proves the existence of a somatosensory coordinate transformation from body surface position into joint angle space. The principles of coordinate transformation, targeting accuracy and transition between the aimed and cyclical parts of the movement can be explained by a simple artificial neural network. In essence, a feed-forward network transforms the 2D stimulus location into the median limb posture of the aiming movement, while the transition from straight to cyclic movement is due to the damping properties of the control circuit.
At the level of the neuromuscular transform of the knee joint, we analysed how the activity of four groups of excitatory flexor motoneurons and both excitatory extensor motoneurons translates into the movement of the joint. For this, we developed a three-stage model that incorporates the neuromuscular transform that converts the motoneuron spike trains into muscle activation (stage 1: activation dynamics), a Zajac-Hill-type muscle model containing three characteristics for active and passive components of muscle force (stage 2: contraction dynamics) and a mechanical description of tendons, moment arms and a damping term (stage 3: joint mechanics). The activation dynamics model was based on a separate set of experiments in which we used a system of two coupled second-order differential equations to model the low-pass characteristics of twitch contraction forces. Two Michaelis-Menten equations were used to model frequency-dependent changes in peak contraction force, necessary to explain the transition from single twitch events to tetanic contraction force. The joint mechanics model was based on literature values, except for the slope of a linear damping term. The parameters of the contraction dynamics model were optimised in a "black box" approach, using pairs of a motor spike train input sequence and the corresponding movement (output sequence) of the joint.
Together with results from neurophysiological experiments, the neuromechanical model illustates how passive forces and co-contraction of antagonist muscles simplify neural posture control and load compensation.
Work done in collaboration with Jure Zakotnik and Tom Matheson.
Walking in mammals is the result of an intrinsic interplay between neurons, muscles, body mechanics and sensors. We use computer simulation as a tool to understand this system. I will describe some experiments where we have used a model of the musculo-mechanical plant to test different hypothesis about how the neural control may operate.
Starting from a basic rhythm generating circuit originating from the work on the lamprey we have studied what additions are necessary to handle walking, and find that surprisingly little needs to be modified.
Swimming due to sinusoidal body undulations is observed across the spectrum of swimming organisms (and Reynolds numbers) from microscopic flagella to fish. The internal force generating mechanisms range from the action of dynein molecular motors within a flagellar axoneme, to muscle activation in lamprey. These active forces are also mediated by passive structural forces in each system. We will present recent progress in building computational models, based upon an immersed boundary framework, that reflect the full coupling of internal force mechanisms with external fluid mechanics in each of these systems.
The neural control system underlying the control of locomotion will be presented, including the intrinsic function of the spinal networks coordinating locomotion, the supraspinal command systems that initiate locomotion and the neural mechanisms underlying selection of behavior at the level of the basal ganglia. In addition, the control of body orientation, orienting reflexes and steering will be discussed.
References:
- Grillner, S, Kozlov, A, Dario, P, Stefanini C, Menciassi, A, Lansner, A, Hellgren Kotaleski, J. (2007) Modeling a vertebrate motor system: pattern generation, steering and control of body orientation. Prog Brain Res. 2007;165:221-34.
- Grillner, S. (2003) The motor infrastructure: From ion channels to neuronal networks. Nature Reviews Neuroscience, 4: 573-586.
- Grillner, S. (2006) Biological Pattern Generation: The Cellular and Computational Logic of Networks in Motion. Neuron 52; 751-766.
- Saitoh, K., A. Menard, S. Grillner (2007) Tectal Control of Locomotion, Steering, and Eye Movements in Lamprey. J. Neurophysiol. 97:3093-3108.
In stick insects, walking is the result of the co-action of different pattern generators for the single legs and coordinating inter-leg influences. The pattern generator for each leg consists of central pattern generators (CPGs) for each leg joint.
We have used a slippery surface setup to study the coordination of single insect legs in the intact stick insect without the effect of substrate coupling. We analyzed the walking pattern of the front middle and hind legs of animals walking on the slippery surface and compared the kinematics of the straight walking legs with those of the curve walking inside and outside legs. The walking pattern was monitored electrically through tarsal contact measurement, and optically by using synchronized high-speed video. The vectors of leg movement are presented for the intact and the reduced preparation. Animals showed the ability to walk in a coordinated fashion on the slippery surface. Upon change from straight to curve walking, the stride length for the inside legs shortens and the vector of movement of the inner legs changes to pull the animal into the curve, while the outer legs act to pull or push it into the turn. In the reduced two-leg and in the single-leg preparation the behavior of the legs remained largely unchanged in the behavioral contexts of straight walking or turning with only small changes in the extreme positions. This suggests that the stepping behavior of the single leg in a given motor program is highly independent not only of mechanical coupling between, but also of the presence of the other legs.
I will review our attempts to build an analytically-tractable, yet biophysically-grounded, neuromechanical model of a running animal, with particular reference to the cockroach Blaberus discoidalis. Building on a sequence of simple mechanical models, we have successively added actuated, axially-sprung legs, jointed legs, and muscles. In doing so we have confirmed the 'preflexive' hypothesis: that feedforward control, coupled with passive dynamics, can yield robustly stable gaits. In parallel work we have modeled the insect central pattern generator and motoneurons. It remains to integrate neurobiology and biomechanics by incorporating models of proprioceptive and exteroceptive sensing. I hope to stimulate a debate on appropriate levels of detail in such integrated models, and, more generally, on their role in the biological sciences.
This is joint worth with J. Schmitt, R. Ghigliazza, J. Seipel, R. Kukillaya, J. Proctor, M. Srinivasan, R. Altendorfer, R.J. Full and D. Koditschek.
Model systems (cat, mouse, lower vertebrates and invertebrates) have provided major insights into mechanisms underlying motor pattern generation. However, these systems have several characteristics not shared by humans, and properly applying data from them requires careful consideration of these differences. We concentrate on two such differences, that such animals are generally small, and often (particularly invertebrates) have slowly contracting and relaxing muscles. Simple scaling shows that muscle forces (including, critically, passive forces) increasingly dominate limb movement as limb size decreases. Small limbs consequently have gravity independent rest positions to which the limb will return, regardless of orientation, in the absence of motor neuron input. Small limbs are also incapable of momentum based movement, requiring instead motor neuron input that lasts as long as the movement (as opposed to human leg swing, which is powered by a brief initial muscle contraction and then continues due to momentum and gravity driven pendulum mechanics). Slow properties result in these muscles acting as slow filters of motor neuron input. This filtering can be great enough that the muscles do not contract in time with the rapid bursting activity of their innervating motor neurons, but instead with other, much slower neural networks that modulate the motor neuron activity. This slowness also results in much of the contractions of these muscles being in the 'no mans' land between the passive and active length-length curves. When load is increased during shortening, shortening of these muscles can therefore continue without sensory feedback induced increases in motor neuron activity.
Animal locomotion control is in a large part based on central pattern generators (CPGs), which are neural networks capable of producing complex rhythmic patterns while being activated and modulated by relatively simple control signals. These networks are located in the spinal cord for vertebrate animals. In this talk, I will present a modeling study carried out together with Jean-Marie Cabelguen in which we model CPGs of lower vertebrates (lamprey and salamander) using systems of coupled oscillators, and test the CPG models on board of amphibious robots, in particular a new salamander-like robot capable of swimming and walking. The goal of the project is to explore three important questions related to vertebrate locomotion: (i) the modifications undergone by the spinal locomotor circuits during the evolutionary transition from aquatic to terrestrial locomotion, (ii) the mechanisms necessary for coordination of limb and axial movements, and (iii) the mechanisms that underlie gait transitions. I will also address the possible role of sensory feedback in shaping the locomotor patterns depending on the physical interactions of the body with different media (friction with ground during walking and interaction with water during swimming).
Rhythmic body movements observed in animal locomotion result from interactions of various dynamical elements, including the neuronal circuits called central pattern generators (CPGs), muscle activation by motoneurons, sensory feedback from receptor neurons, body biomechanics, and dynamics of the surrounding environment (e.g. air, water, ground). Feedback control theory provides an integrated view of dynamic interactions and a systems-level framework for understanding the animal locomotion mechanism. Our research has focused on feedback control principles underlying undulatory swimming of leeches. This talk proposes the following hypotheses on the mechanism of animal locomotion: (i) the frequency of body undulation during swimming is chosen close to a resonance mode of the body dynamics, and (ii) the gait (i.e., phase pattern) is chosen to optimize a criterion under the dynamical constraint of the body-fluid interaction. These hypotheses are motivated by observations of leeches "swimming in air" where a body hanged in air by threads oscillates at a frequency near that of normal swimming in water, but exhibits almost no traveling wave. We will provide evidence supporting the hypotheses, by performing theoretical analyses of a mathematical model of leech swimming developed through combinations of physiological experiments and first principles in physics.
New numerical methods are described for the approximate solution of systems of equations arising in mathematical models of the neurodynamics of various modes of animal locomotion. The mathematical models usually involve dynamical systems, which are sometimes large scale. Moreover, feedback of some kind is also normally present, so that the corresponding control problems have to be solved. The relevant systems are described mathematically in terms of differential or differential-algebraic equations, which are frequently stiff systems involving different time-scales. Consequently, severe numerical difficulties in the computations are likely to be encountered, which means that standard finite difference or finite element methods are not effective. We describe recent advances in the construction of robust numerical methods for large-scale dynamical systems with controls. These are robust in the sense that the numerical approximations behave uniformly well regardless of the range of scales present, which is not the case with the numerical approximations generated by standard numerical methods.
Muscle physiologists typically study the behavior of muscle under a limited set of conditions, such as isometric tetanus or isotonic shortening, which rarely apply to movements of freely behaving animals. While investigating ballistic prey capture behavior in toads, we re-discovered the usefulness of an old technique, the load-clamp, for quantifying contractile and elastic properties of muscles and their connective tissues under physiologically relevant conditions. This technique allows muscle properties to be studied under a wide range of conditions, particularly those in which muscles develop force against a resisting force, and shorten when the resisting force is reduced. Using this technique, we developed an elastic recoil model of muscles and connective tissues during ballistic movements. The model accurately predicts the observed amplitude and velocity of movements given only the duration of muscle activation prior to unloading and the external load. It predicts elastic behavior during active shortening for several muscles (depressor mandibulae, sartorius, extensor digitorum longus, soleus) in different species (frog, mouse). In addition, it predicts the elastic behavior of muscle under isometric and isotonic conditions. At the level of the whole organism, the model predicts that appendages of smaller animals will operate at higher stiffness, and hence at greater frequencies, than those of larger animals. The model demonstrates that actively shortening muscles exhibit dynamic stabilization to perturbations in load without requiring neural input. It also suggests that control of rapid movements may require specification of relatively few variables.
Work done in collaboration with Jenna Monroy, Leslie Gilmore, Theodore Uyeno, and A. Kristopher Lappin.
Computer simulations are being used increasingly to gain insight into the neurobiology and biomechanics of walking in humans and quadrupeds. In general, these simulations are based on very limited knowledge of the neural systems generating the motor patterns for walking, the properties of muscle producing the movements, and the mechanics of muscle action. Nevertheless, these simulations have yielded valuable insights into some low-level features of mammalian locomotion, especially the biomechanical functions of specific muscles and the role of afferent signals in regulating phase transitions of the step cycle. The most obvious shortcoming in developing more versatile and complete simulations of walking is a serious lack of knowledge of the underlying neurobiological mechanisms. Despite enormous effort, we still know little about the cellular and network properties of pattern generating networks in the mammalian spinal cord, and even less about how these networks are controlled by descending signals from the brain during walking. In this presentation I will review the limited data we currently possess, and attempt to identify areas in which additional data would facilitate the development of useful simulations.
We use methods from dynamical systems theory to analyze movement of /Blaberus discoidalis/ cockroaches. One of our key objectives is to derive dimensionally reduced models that describe the biomechanical synergies used by an animal steadily running on flat ground. By modeling the motion as a stable periodic orbit in a body centered frame of reference, we may apply Floquet theory to the problem. In the absence of noise, the theory predicts a change of coordinates which rectifies the motion transverse to the orbit to a time invariant linear system with modes that decay exponentially. These Floquet modes can be divided into those that are highly damped and those that are weakly damped. Preliminary results give evidence for few weakly damped modes, and for many highly damped modes that decay in less than a stride. We hypothesize that the weakly damped modes form a template for the neuromechanical control of locomotion.
We describe our use of diverse tools from motion tracking, numerical analysis, visualization and geometric statistics to fit these periodic orbit models to video recordings of running cockroaches. Our focus is on the numerical estimation of a phase variable and of the linearized first return map, with quantified levels of statistical confidence in the presence of noisy data.
The ability of animals to negotiate unpredicted barriers in natural terrain makes them attractive models for robotic design. Animals evaluate objects in their path using sensors on their head, then use that information to formulate commands that ultimately re-direct leg movements. In order to understand this process in insects, we employ a range of behavioral and neurobiological studies directed at both thoracic local control circuits and brain centers. These studies are augmented by robotic hardware models that allow us to test and refine biological hypotheses and examine implementation under real physical conditions.
Our research begins with behavioral observations. Cockroaches deal with blocks in their path by first evaluating the object with antennae and other sensors, then rearing up to an appropriate height for climbing. If the block is replaced with a shelf the insect now has a choice. If the antennae contact the shelf from above, the insect will climb over, while contact from below will cause it to tunnel under the barrier. Antennal contact of a wall may generate turning movements. Other sensors such as vision also affect decisions and all these data must be processed within the insect's brain. Insects that have experienced bilateral lesion of circumoesophageal connectives, that disconnect the brain from the thoracic ganglia, deal with barriers in a less controlled manner. These animals crash into walls, then force themselves around or over them by brute force. Lesions within the brain also generate abnormal behaviors if they involve a region designated as the Central Complex (CC).
We then examine both motor and leg joint kinematics associated with turning by studying cockroaches that are tethered over a lightly oiled plate. In turning, leg joints shift from symmetrical (left-right) movements to asymmetrical actions. Although these are profound changes, our observations suggest that they may arise through a process in which descending commands alter a few critical feedback circuits then allow local reflexes to push the leg toward a new stable state through a cascade of changes.
Our behavioral observations indicate that mechanical stimulation of antennae provide much of the necessary information for evaluating barriers, and lesion studies implement the Central Complex (CC). We, therefore, investigated responses of CC units to mechanical stimulation of antennae. We inserted 16-channel extracellular probes into the CC of restrained cockroaches. In these recordings, we isolated 5-20 units in most experiments. In all, we examined over 250 units and about half of them responded to stimulation of either antenna, with about one-third being biased to one side. Most of these units also responded to visual stimuli. Thus, we found a large multi-sensory population of neurons associated with the CC that could be used to generate the descending activity necessary to alter local circuits and re-direct leg movements. Finally, in tethered insects, we can observer brain activity in relation to actual leg movement. Neurons recorded in the CC show activity associated with step patterns. Furthermore, stimulation in these regions can alter movement. We are currently developing a robotic leg that simulates joint movements of a tethered cockroach and is controlled by feedback circuits that have been documented in insect preparations. This "hardware model" will help us to formulate and test hypotheses of the mechanisms by which brain circuits re-direct leg movements to deal with barriers.
One general class of goals is the prediction of human or animal coordination choices from a given physical architecture. This would be useful for the diagnosing and fixing of health problems as well as for the generation of animal like robots (which, to be animal-like, must be robust, smooth, and low in energy use). Candidate principles for generating such a prediction include A. Wiring/evolutionary constraints: animals do what they do because their electrical hardware has evolved a certain way. B. Stability: coordination choices are based on the robust insensitivity to perturbations (of the model, of the sensors and actuators, or of environmental disturbances). C. Energetics: given the body layout and the motion goals the motions minimize some measure of effort. D. Passive mechanisms: bodies do what they do naturally.
I will review some general thoughts about these approaches based on a few robotics-like examples including examples from walking simulations and robots, hopping simulations and robots, bicycles and primitive control theory. Some observations: 1) passive strategies and energy minimizing strategies have some overlap, 2) Given reasonable sensory feedback, short reaction times, and low noise both stability and robustness seem easy to achieve and thus are not useful for making predictions. 3) Given the huge range of possible complex behaviors of neural systems, even small systems, evolutionary constraints do not seem promising for making general predictions. Thus the only reasonable candidate class of predictive theories seem to be those based on some kind of effort minimization and performance optimization. On the other hand, full blown optimal feedback control (e.g., value functions etc) seems to demand too much information management. Rather, optimal trajectories with simple feedback seems to have both predictive ability and a way to make functional control designs.
In animals, control of walking in rugged terrain requires to incorporate different issues, as are the mechanical properties of legs and muscles, the neuronal control structures for the single leg joints, the mechanics and neuronal control structures for the coordination between legs, as well as central decisions that are based on external information and on internal states. This applies correspondingly to all similar technical applications as e.g. walking machines. Walking in predictable environments and fast running, to a large degree could rely on central pattern generators (CPG) or even solely on muscle mechanics. In contrast, slow walking in unpredictable terrain, e.g. climbing in rugged structures, has to rely on systems that monitor and intelligently react to specific properties of the environment as well as to the consequences of the interactions of the walker with its physical environment.
An arthropod model system that shows the latter abilities is the stick insect on which this presentation will be focused. An insect, when moving its six legs, has to control at least 18 joints, three per leg, and therefore has to control at least 18 degrees of freedom (DoF). As the body position in space is determined by 6 DoFs only, there are 12 DoFs open to be selected. Thus, a fundamental problem is as to how these extra DoFs are controlled. Based mainly on behavioral experiments and simulation studies, but also including neurophysiological results, the following control structures have been revealed.
Legs act as basically independent systems. The quasi-rhythmic movement of the individual leg can be described to result from a structure that exploits mechanical coupling of the legs via ground and body. The timing of step phase transitions is neither determined by the action of CPGs within the leg nor by CPGs of the leg joints. Rather, reflex chains triggered by specific sensory feedback at the appropriate phases will generate sensible switching between the step phases. Furthermore, neuronally mediated influences act locally between neighboring legs, leading to the emergence of insect-type gaits. The underlying controller can be described as a free gait controller. Cooperation of the legs being in stance mode is assumed to be based on mechanical coupling plus local positive velocity feedback controllers. These controllers, each acting on an individual leg joint, transform passive displacement of a joint into active movement, generating synergistic assistance reflexes in all mechanically coupled joints. A coherent action of the leg joints of each leg being in swing is assured by neuronally mediated interjoint reflexes.
This architecture of the controller is summarized in the form of the artificial neural network, WalkNet. It consists of several modules of small networks. Although the demands on the single networks are high, each of the network modules could be kept very simple because they all are embodied, i.e. situated in the physical environment of the animal. Utilisation of the external loop via the periphery (the sensory-motor system and its interaction with the physics of the habitat) allows for such simplification. For example, in the case of the SwingNet module, this means that no explicit trajectory is precalculated but that a momentary change of the ongoing swing movement is generated only on the basis of the actual sensor data. This design also allows the emergence of new properties such as flexible reactions to disturbances or to failures in reaching ground. At the system level, this design gives rise to emergent behaviours. In addition to producing stable and robust gaits without a master timer, the system can stand up again by itself and resume proper walking after stumbling. Exteroceptive feedback is exploited for global decisions as are e.g. direction, curvature, and velocity of the walk. In the talk I will demonstrate the usability of this controller architecture by means of dynamic simulations and hardware implementations.
Work done in collaboration with Holk Cruse, Volker Dürr, and Axel Schneider. Supported by grants from Deutsche Forschungsgemeinschaft, European Community, and German Ministry of Technology.
During the last four years, a number of simplistic robotic platforms were developed at the Lauflabor Locomotion Laboratory at the University of Jena, Germany. The concept behind these systems can be understood in the framework of the conceptual models on gait stability. With the exception of the MarcoHopper - which addresses reflex mechanisms in the leg - all other robots do not require sensory feedback in order to achieve steady locomotion. However, sensory feedback can be used to further enhance gait stability.
In this talk the interplay of robot experiments, conceptual models and human trails will be demonstrated at selected system levels. This includes effects of leg segmentation, gait pattern generation, impact management, trunk stability and muscle-reflex dynamics during locomotion. We will address issues which are specific to technical systems and compare them to solutions found in animals and humans. Finally, some implications for future robot developments and prosthetic or orthotic devices will be given.
Swimming in the anuran frog, Xenopus laevis, changes dramatically during the organism's life. A tail-based undulatory strategy, established early in development around the time of hatching, undergoes a period of maturation when the flexibility of the larval swimming pattern increases. Later, a limb-based system appears, initially assisting the tail in generating propulsion before superseding the tail system at metamorphosis.
I will review the nature of the central pattern generating (CPG) networks responsible for generating swimming and how they are modified during development to accommodate the behavioural requirements of the organism. The basic network assembled in ovo produces a motor rhythm in which myotomal motor neurons discharge a single impulse per cycle. I will present recent evidence that electrical coupling between motor neurons is responsible synchronization of motor activity. After hatching the larval swimming rhythm become more burst-like and flexible. The role of a range of neuromodulators which are important in conferring this flexibility including serotonin, noradrenaline and nitric oxide (NO) will be reviewed. NO functions as a metamodulator, governing how brainstem nuclei modify the spinal locomotor circuitry.
The metamorphic period is characterized by a gradual switch from tail- to limb-based swimming. The emerging limb network is initially co-opted into the existing tail circuit before adopting its own cadence and independence. New populations of NO generating neurons appear in the spinal cord, by which time NO's role in modulating swimming switches from inhibitory to excitatory.
Supported by the BBSRC and the Wellcome Trust.
Standing balance control is a complex sensorimotor task that is fundamental to the performance of other motor behaviors. Neuromechancial principles for control of posture and balance are little understood, as they involve integration of multiple channels of sensory input and motor output. Descending control of postural response appears to be rather low-dimensional, as muscle activity and biomechanical outputs can be described using just a few parameters related to task-level variables. These data might suggest that the control of balance is simple, as they are aptly described by simple, conceptual, "template" models. However, there are no complex, anatomical, or "anchor" models that can actually stand up using physiological elements - including our own. Moreover, experimentally we observe a wide degree of variability in postural responses across trials and individuals, suggesting that the biological systems are quite robust to variations, whereas our musculoskeletal models are not. What are they missing?
We hypothesize that postural stability requires precise coordination among hierarchal, redundant neuromechanical elements, and that the contributions of each are flexibly adjusted by the nervous system as appropriate to a particular situation. That is, the "simple" task-level commands are only functional if appropriately subserved by neurally-modifiable spinal and peripheral mechanisms for quiet standing. Therefore, we predict that the nervous system modulates interactions between hierarchically organized neuromechanical elements that contribute to feedback neural processes required for reacting to postural perturbations and feedforward neural processes that adjust the intrinsic mechanical stability of the musculoskeletal system. We have evidence in both normal and impaired balance control, of shifts along this continuum between neural and mechanical computations for mitigating disturbances to balance. Our neuromechanical modeling efforts also demonstrate that task-level feedback, postural tone, and postural configuration cannot be independently modulated to produce stable posture. These ideas extend to all motor tasks. I propose that motor control principles adequate for allowing us to reproduce real functions will only be revealed if all levels of the neuromechanical hierarchy, and their interactions, are understood.
In fishes, undulatory swimming is produced by sets of spinal interneurons constituting a central pattern generator (CPG). The CPG can produce the basic pattern for locomotion in the absence of sensory information, but is strongly affected by sensory input. For instance, proprioceptive feedback from mechanosensory "edge cells" on the margin of the lamprey spinal cord can reset the CPG's rhythm or entrain it to a different frequency. The CPG's output, in turn, activates the muscles, bending the body, and providing proprioceptive input back to the CPG itself. This feedback loop was studied in two ways. First, the input-output relationship between sensory information and the CPG rhythm was investigated during fictive swimming in the isolated spinal cord. The cord was bent sinusoidally back and forth at several points along its length. Bending at caudal segments entrains the CPG so that each side starts a burst just before it is maximally stretched, which is approximately the same phase relationship observed between muscle activity and bending in freely swimming lampreys. Bending at rostral segments, in contrast, results in bursts on each side just after that side is maximally shortened and is beginning to stretch, nearly 50% out of phase with the pattern observed in free swimming. Second, the closed-loop behavior of the spinal cord was investigated by filtering the CPG bursts (its output) in real time with a computer and using the filtered bursts to determine the bending applied to the spinal cord (the CPG input). Filtering was done with a variable phase lag linear filter to test the CPG's stability with different phase relationships between motor output and movement. Additionally, the resonant properties of the lamprey body were simulated in the computer to determine if the CPG frequency would converge to the body's resonant frequency, which would be useful for efficient swimming.
Work done in collaboration with A.H. Cohen.
A theme of my work is related to the questions: How does the neuromechanical system meet the necessary and sufficient conditions for complex function? and What specific contributions come from passive (e.g., tissue) and active (e.g., muscles & neurons) components of dexterous manipulation as a sample complex neuromuscular system? In this presentation I explore those questions in the context of a simple and fundamental aspect of manipulation: making abrupt contact with surfaces to produce fingertip force (as in grasping objects), and producing both motion along a surface and force against it. These two tasks reveal a surprisingly complex and time-critical control strategy, and emphasize that these fundamental aspects of manipulation require cortical involvement. I conclude by underscoring other instances where the complexity of the tendons of the fingers collaborates actively to enhancing the mechanical ability of the fingers, thus providing a clear example of brain-body co-evolution.
Fish swim by generating waves of muscle activation which travel toward the tail, which in turn generate waves of body curvature. The body curvature waves travel more slowly than the activation waves, and this leads to an increasing delay between muscle activation and muscle shortening. In consequence, near the tail muscle is active partially while lengthening. In this study we have investigated the features responsible for this changing phase lag, by incorporating a physiological model of muscle within a model of passive body and fluid mechanics, and studying the consequences of altering various features of the combined model. We have found that the difference in wave speeds requires the viscoelastic properties of the body, body taper, and the dependence of generated force on muscle length and rate of change of length.
Work done in collaboration with Philip Holmes.
Many animals have sensory receptors that detect forces in the legs and use this information to generate and adapt posture and locomotion. Recent studies of campaniform sensilla, sense organs that detect forces as strains in the exoskeleton of insects, have demonstrated that individual receptors show considerable specificity in the parameters of load that are signaled. Neurophysiological recordings in freely moving animals and modeling studies have demonstrated: 1) the presence of signals of unloading as well as loading, both of which are temporally linked with movement velocity during postural perturbations; 2) the signaling of body load as a continuum which changes from modulation of excitatory inputs during normal load variations to the elicitation of inhibition during large or rapid load decreases; 3) the dependence of force feedback upon leg position in walking, as supported by studies using finite element analysis to model receptor discharges in walking. These studies suggest that the specificity of sensory discharges reflects both the morphology and behavioral use of the leg. Comparable tuning of sensory signals to leg and body structure may be advantageous in both animals and walking machines.
Poster Presentations
Muscles transform neuronal control signals into movement. In addition they constitute generic feedback controllers, as their force depends on the movement created. A combination of simulating muscle properties and animal physics provides a tool to investigate the integration and eects of muscles in respect to locomotion control.
We use a Hill-Type muscle model of the middle leg Extensor tibiae of the Stick Insect (Carausius morosus). It is based on the detailed physiological analysis of Guschlbauer et al.[2]. We will present the modeling of core muscle features like force-length and force-velocity dependency as well as activation dynamics.
A simple leg controller derived from neurophysiological data can be used to generate cyclic stepping movements of a single leg [1]. Muscle properties however in uence the performance of this movement. A comparison with the data from 2004 (with its highly simplistic muscle model) illuminates the role muscle properties can play for leg stepping control and how they eect the resulting movement.
References:
- Ekeberg, Blumel, Buschges (2004) Dynamic simulation of insect walking. Arthropod Structure & Development 33: 287-300.
- Guschlbauer C., Scharstein H., Buschges A. (2007) The extensor tibiae muscle of the stick insect: biomechanical properties of an insect walking leg muscle. Journal of Experimental Biology, 210: 1092-1108.
Understanding neural control of locomotion in biology and designing efficient controllers for walking machines remain a challenging tasks. In both cases current research has shown the indispensability of taking into account the interplay of (neuro-)controllers, body properties and the senori-motor loop. As a consequence of this complex interaction it is hard, if not impossible, to intuitively make a clear distinction between contributions of the involved subsystems. Simulations and biorobotics are proposed as tools to make new hypotheses which can be tested in biology. To permit a comparison of biological and artificial (neuro-)controllers on an operational level it is a prerequisite to explicitly take the essential properties of these subsystems into account. With my poster I address the question of how the neuro-muscular transform, which accounts for differences between motor neuron output and resulting motor behaviour, changes the requirements for a (neuro-)controller of a 3DOF leg. Techniques from evolutionary robotics using the artificial life approach are employed. A large number of different neuro-controllers for a single-leg of a hexapod robot are evolved in simulation under different pertubation conditions (sensor/motor noise, external forces): 1. with direct mapping of motor neuron outputs to the dc-motor and 2. with mapping of motor neuron outputs via a muscle model. Evolved controllers are compared in terms of number of units, connectivity, sensors used, function and resulting behaviour. To exclude simulation artifacts and to show applicability for robotics resulting controllers (with and without muscle model) are tested on a physical walking machine.
